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A281301 Trajectory of 1000004999700144385 under the "Reverse and Add!" operation. 9
1000004999700144385, 6834415079694144386, 13668830049399288772, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771, 3542550333873429453542, 5996099577656760005995 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
1000004999700144385 is the largest of the first 225 numbers that require exactly 259 steps to turn into a palindrome (see A281390). The sequence reaches a 119-digit palindrome after 259 steps (see b-file). The number was obtained empirically using computer algorithms and was not reported before.
Row 1000004999700144385 of the array in A243238. - Felix Fröhlich, Jan 21 2017
REFERENCES
Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975).
LINKS
Sergei D. Shchebetov, Table of n, a(n) for n = 0..259
Jason Doucette, World Records
Yutaka Nishiyama, Numerical Palindromes and the 196 Problem, International Journal of Pure and Applied Mathematics, Volume 80, No. 3, 2012, 375-384.
R. Styer, The Palindromic Conjecture and the Fibonacci Sequence, Villanova University, 1986, 1-11.
C. W. Trigg, Palindromes by Addition, Mathematics Magazine, 40 (1967), 26-28.
C. W. Trigg, More on Palindromes by Reversal-Addition, Mathematics Magazine, 45 (1972), 184-186.
Wikipedia, Lychrel Number
196 and Other Lychrel Numbers, 196 and Lychrel Number
FORMULA
a(n+1) = a(n) + rev(a(n)).
EXAMPLE
a(1) = 1000004999700144385 + 5834410079994000001 = 6834415079694144386.
MATHEMATICA
NestList[#+IntegerReverse[#]&, 1000004999700144385, 10] (* Harvey P. Dale, Dec 24 2021 *)
PROG
(PARI) terms(n) = my(x=1000004999700144385, i=0); while(1, print1(x, ", "); x=x+eval(concat(Vecrev(Str(x)))); i++; if(i==n, break))
/* Print initial 9 terms as follows: */
terms(9) \\ Felix Fröhlich, Jan 21 2017
CROSSREFS
Sequence in context: A256312 A173445 A281390 * A286481 A168334 A358020
KEYWORD
nonn,base
AUTHOR
Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 21 2017
EXTENSIONS
a(9)-a(10) from Felix Fröhlich, Jan 21 2017
STATUS
approved

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Last modified April 17 15:33 EDT 2024. Contains 371764 sequences. (Running on oeis4.)